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LIBRARY OF CONGRESS 

019 820 178 9 



HoUinger Corp. 



An Experiment To Determine 
The Number of Repetitions 

Necessary to Memorize and Retain 
With Maximum Certainty 

A Miscellaneous Collection of Facts 



A THESIS presented to the Faculty of the Graduate School 
Of the UNIVERSITY of PENNSYLVANIA 

In Part Fulfilment of the Requirements for the 
Degree of Doctor of Philosophy 

BY 

A. L. WAGNLR, Ph. D. 
Nesquehoning, Pa. 

MAY 1910 



/ 



"'i 



V 



.^u^- 



The Number of Repetitions Necessary to Memorize 

And Retain With Maximum Certainty 

A Miscellaneous Collection of Facts 

INTRODUCTION 

The Jesuit Scliools for more than a century were 
the unrivaled leaders in the educational world. " Their 
aim was to prepare for leadership in the evangelization 
of humanity. Their entire system was based upon the 
principle that it is better to teach a relatively small 
ain()unt in a thorouoh manner, than to give an in- 
definite impression of a much larger quantity. They 
gave frequent reviews. Kach day began with a review 
of the things taught on the previous day; each week 
ended with a review of the things presented during this 
time; each year was closed with a review of the work 
done that year; and the whole course was then reviewed 
by teaching it. The entire system had as one of its 
leading characteristics frequency of reijetition accom- 
panied by i)relecti()n and erudition. They succeeded in 
securing intellectual development and tlie results de- 
sired were always certain. 

After the Jesu.its, Ratick was the first to realize 
that educational method must secure maximum cer- 
tainty of recall, and that this is obtained best by 
reijetition. One thing at a time and that often repeated 
was one of his maxims. He had the sagacity to foresee 
that successful mastery necessitated a relatively small 
content, though he failed to construe "one thing" as a 
basal element in thinking, a point or unit of subject 
matter, and often repeated and re-repeated his "one 
thing" until some things were repeated to death. He 
was not sagacious enough, however, to perceive the 
wisdom of using the children of his sch<M)l to determine 
the conditions under which repetition will most advan- 
tageously secure maximum certainty of recall. 



The next attempt that was made ahjiii; the lines of 
repetition to secure mastery was made by l^rofessor 
Cornman of Columbia in connection with the spelling. 
In the investigation hereinafter described, an attempt 
is made to secure information along the same lines. 

Practical pedagogy makes it necessary that we 
know more definitely how to secure the excellencjps of 
the method of repetition used by the Jesuits and Katick 
and how to avoid its defects. This knowledge can not 
be gleaned by the application of theoretical psychology 
but must be derived frotti facts scientifically determined. 

That scientific methods should be used in procur- 
ing pedagogical knowledge or in deriving facts ujjon 
which principles may l)e formulated, ma\- seem strange, 
but it is in no way more unusual than the use of the 
same methods iii any other field of human endeavor. 
The good teaching which we have will be improved as 
soon as principles based upon facts scientifically deter- 
mined are applied in the practical work of the school 
room. Valuable indeed to any teacher will it be to know 
the number of repetitions needed b^^ children, under 
ordinar3' circumstances, to learn things, and equally 
valuable will it be to know how frequent the repetitions 
must be in order that the facts may be retained when 
once they are learned. 

In the experiments of which a description follows, 
an attempt w^as made to determine: 

1. How many repetitions are necessary to secure 
the mastery of facts with maximum certainty; and 

2. At what intervals the repetitions must occur 
in order that the mastery, when once secured, 
may be retained. 



8 
THE FIRST EXPERIMENT. 

When the experiment was first begun, it seemed reason- 
ably certain to the experimenter that the written form of repe- 
tition would be the most desirable. Questions, the answer 
to which could be given in a single sentence, or even a single 
word, were selected and given in order to avoid the element 
of judgment in determining the relative worth of the answers, 
and in order to insure, with maximum certainty, that the 
answers given would be either entirely correct or incorrect. 
Instead, however, of giving the single word desired as the 
answer to the question, a number of the children substituted 
other terms from which it was impossible to determine whether 
they retained the major portion of the original presentation ; 
or whether, as the word used in answering often indicated, 
they retained but a small portion of the content of the word 
desired for an answer which the original presentation was 
intended to give. In a number of instances, the words which 
were used in answering the question may have or may not 
have signified that the original presentation was retained. In 
writing the names of two rivers of Africa as the "Murray of 
Darling" instead of the Alurray and Darling, unless one is will- 
ing to assume that the placing of the "of" instead of the "and" 
was a mere slip of the pencil, the conclusion that much of 
the original presentation was no longer functioning is inevi- 
table. A similar illustration occurred with the words "llanos." 
"lepidodendron." "Locust Mt." and others. Were I to try 
the experiment again, other forms of writing the answer than 
writing merely one word would be used. 

The presentation of the facts in each case was as clear 
and as full as the presenter could make it. All forms of pres- 
entation were used that could be thought of. The facts to be 
remembered were illustrated by pictures, stories, and drawings. 
Every form of apperceptional contribution known to be avail- 
able was utilized. 

Some of the repetitions were called for by the teacher, 
others by the experimenter. That the number of errors is as 
small as it is, may be due to the fact that the desire on the 
part of the teacher to have her room make a good showing was 
stronger than her desire to have the experiment scientifically 
accurate. 

Only such facts were presented as seemed to be unknown 
to the children with whom the experiment was tried. Some 
of these were selected because of their local significance, and 
because it was somewhat difficult to find facts with which chil- 
dren of an entire group who had completed an elementary 
geography and history were unfamiliar. This is especially true 
of the facts that were used with the seventh and eighth grades. 

All facts were presented at one sitting by myself. This 
required three-fourths of an hour for the fifth, sixth, and 



4 
eighth grade, and one and one- fourth hours for the seventh 
grade. When the fact had been presented by the experi- 
menter, tlie answer desired for future repetitions was written 
upon the blackboard by himself, and upon a slip of paper by 
the children. When all the facts had been presented these 
l)apers were collected. At each repetition the questions were 
asked by the experimenter or the teacher, and the answers were 
written upon slips of paper by the children in the same manner 
as spelling words are usually written. The errors were then 
marked by the children, each retaining his or her own slip, the 
experimenter or the teacher repeating the correct answers in 
their numerical order. Each child making an error was re- 
quired to write the correct answer at the clo.se of the exercise. 
Before the papers containing the children's answers were filed 
and before the exercise was over all papers were looked over 
by the experimenter or the teacher to avoid having mistakes 
pass unnoticed. The number of repetitions as indicated on the 
sheets containing the results means the number of times 
that they were written on paper. exce]it in the eighth grade 
where they were repeated orally. 

The ])apers containing the results of the first repetitions 
showed a lamentable lack on the part of the slow learners to 
g(>t the correct spelling of the terms required in the answers. 
No attem])t was made to secure correct spelling by having a 
repetition of the fact. In giving the correct answer while the 
errors were being marked the teacher or the experimenter 
spelled the word instead of saying it. It is possible that this 
form of oral repetition aided in impressing the fact to be re- 
membered as well as the spelling of the word that stood for 
it. It was necessary to spell the answers five times with the 
sixtli grade folks in order to secure maximum correctness of 
spelling, while with the seventh it required but three, and with 
the fifth two. 

Tlic questions which were given to the fifth grade with 
tlu' answers that were desired follow: 
[. What important geographical circle crosses South America 
near the mouth of the Amazon River? The Equator. 

2. What important geographical circle crosses South America 

near the location of the city of Rio Janeiro? The 
Tropic of Capricorn. 

3. What season do they now have a t Buenos Ayres? 

Autumn. 

4. Wh'dt ocean borders the eastern side of South America? 

The Atlantic. 

5. What island at the southern extremity of South America? 

Terra del Fuego. 

6. What cape at the southern extremity of this island? Cape 

Horn. 

7. What is the largest river of South America? Amazon. 



8. What strait between Terra del Fuego and South America? 

Strait of Magellan. 

9. What is the island at the mouth of the Orinoco River 

and for what is it noted? Trinidad, noted for pitch. 

10. Wiiat mountains along- the western coast of South 

America ? Andes. 

11. How are the summits during the entire year? Snow 

covered. 

12. What three important minerals are found in these moun- 

tains? Gold, silver and copper. 

13. . What three animals inhabit the Andes regions? Condor, 

llama and alpaca. 

14. Name two highland regions of South America. Andes 

and Brazilian. 

15. Where is the rainiest region of the world? Along the 

Amazon. 

16. Name three valuable trees that grow in South America 

Mahogany, rosewood and india-rubber. 

17. What is the name given to the plains along the Orinoco 

River ? Llanos. 

18. What two seasons do they have in Venezuela? The Rainy 

and the Dry. 
ig. What name is given to the plains along the Amazon? 

Silvas. 
JO. Alxmt h(i\v many miles from the most northern to the 
most southern point of South America? About 1500. 
A glance at the (piestions will show that they all refer 
to South America and that there is nothing like a logical order 
in their arrangement. The answers desired to three of them 
require three words, similar in the sense that three of these 
are mineral products, three are the names of animals, and the 
three remaining ones the names of trees. The etTect of this 
associati(Mi will be noted in the results. 

The (|uestions with the answers that were desired which 
follow are the ones that were given to the sixth grade: 

1. About how large is Australia? About as large as the 

Ignited States, about 3 1-2 million square miles. 

2. How is the interior portion of the Australian continent 

with respect to heat and moisture? It is a desert. 
T,. What vahiable mineral is extensivelv mined in Australia? 
Gold. 

4. What is the leading occujiation in New South Wales? 

Stock raising. 

5. Sydney has an extensive trade with what city in the 

United States? San Francisco. 

6. To what race do the native tribes belong? Ilamitic or 

Black Race. 

7. Name three important trees of Australia. Bread-fruit. 

cocoa-palm and banana. 



() 

8. What is exported from South Australia? Wool, grain 

and copper. 

9. What is the religion of the native tribes? Cannibalism. 

10. Name two of the most noted cities. Melbourne and Syd- 

ney. 

11. How are the Australian colonies united? Into the com- 

monwealth of Australia. 

12. Alx)ut what is the latitude of Melbourne? About 40 de- 

grees South latitude. 
i\. What three valuable fruit trees grow in Australia? Ba- 
nana, bread-fruit and cocoa-palm. 

14. By what kind of people was Australia colonized? English 

convicts. 

15. When was the Australian Commonwealth established? 

Jan. 1, 1901. 

16. What are the two most important rivers of Australia? 

Murray and Darling. 

17. How far from Australia are the Fiji Islands? 1200 

miles east. 

18. What island near the southern coast of Australia is 

covered with dense forests? Tasmania. 
IQ. In what city of Australia did the lady live who recently 

visited our school? Ballarat. 
20. What is the principal animal native to Australia? The 

kangaroo. 
The (piestions that were used with the seventh grade were 
those that follow: 

1. Al)out what is the area of Mauch Chunk Township? 

Twenty scpiare miles. 

2. At the base of what mountain is this school building? 

Sharp. 

3. What mountain on the opposite side of Panther Creek 

Valley ? Locust. 

4. How high above the sea level is the Lehigh River at Le- 

high Gap. 389 feet. 

5. Atxiut how high above the sea level is Mt. Pisgah? 1340 

feet. 

6. What is the meaning of Nesquehoning? Narrow Valley. 
7. At what place was Car))oti Counix' first settled? At 

( Jnadeii Hutten. 

8. Write the name of the religious sect and the leader of 

those who made the first settlement. Moravians, 
Zinzendorf. 

9. Indians from what two tribes did the Moravians try to 

convert to Christianity? Delawares and Mohicans. 

10. \\'hat was the name of the family that the Indians carried 

into captivity? Gilbert Family. 

11. What relic of this captivity is still to be seen in Mauch 

Chunk? A Moccasin. 



12. Where was the lirst white man's home built in Mauch 

Chunk Township? Lausanne. 

13. The boyhood of what famous artist was spent at this 

place ? Rothermel. 

14. 1'() what man of Washington's army did Lydia Darrh 

give the information that the British generals had 
planned an attack on the Americans in her house? 
Colonel Craig of Carbon County. 

15. Wlio is the most influential man connected with the his- 

tory of Carbon County? Asa Packer. 

16. What important rock strata have their outcrop at Mauch 

Clumk? Mauch Chunk Red Shale. 

17. What layer of rock strata forms the top and the bottom 

of the coal measures? Pottsville Conglomerate. 

18. What is the thickness of the coal measures? 1855 feet. 

19. What is the name of the plant that formed the larger part 

of these coal strata? Lepidodendron. 

20. What is coal? Locked up sunlight. 

It will be observed that the questions for this group are 
questions that deal with facts that have only local value, and 
that all of them were extremely valuable and significant to 
the group of children to whom they were given. Not one of 
the group had previously had any idea as to the area of the 
township in which they lived. Questions i and 2 referred to 
the two mountains which enclosed the valley in which the 
children lived. The names presented are those that were 
ai:)plied by the Pennsylvania Geological Survey. A number 
of the children of the group had names for these mountains 
that they had gotten by tradition but the names were as various 
as they were numerous. The effect of this learning another 
name for the same thing was not noted as carefully as it 
should have been, but the answers to these two questions at 
least were not different enough from the others to make them 
especially noticeable. 

Not any of the children had any idea of the height of the 
mountains in the midst of which they lived. In the presenta- 
tion of ([uestions 4 and 5 the height of a number of the moun- 
tains in the county was told to the children but only the 
highest and the lowest point was required. The remember- 
iiig of these numbers presented no unusual difficulty, and the 
time of forgetting was too short to really determine, though 
it is possible that the names would stick longer than the figures 

Questions 7 and 10 refer to Indian massacres and raias 
that were made on the inhabitants of the region after the 
defeat of Rraddock. The stories of these massacres with 
their ethical significance was ,given during their presentation. 
The same is true of 8. 9 and ii. 

The story referred to in 14 was new to nearly all of the 
children, and Colonel Craig's connection with it they had never 



8 
known, though a number of them knew many of the Craig 
descendants. 

With number 15 was presented the navigation of the Le- 
high, the buihUng of the Lehigh Valley Railroad and the found- 
ing of Lehigh I'niversity. 

The geological strata referred to in the remaining ques- 
tions were exjyfained and illustrated by drawings and examples, 
and attention was called to a collection of strata near tlie school 
building where the rocks which were once flat have been 
tilted into an almost vertical position and attain to an altitude 
of over 1400 feet. This illustrating and explaining was es- 
pecially true of questions 19 and 20. 

The questions used with the eighth grade were given 
about the time the group was having its final review in geog- 
raphy. It was, therefore, somewhat difficult to select geo- 
graphical questions with which the entire group was entirely 
unfamiliar. The questions that follow are the ones that were 
used : 

1. What is proved by the shadow which the earth casts on 

the moon? That the earth is round. 

2. Name the three planets nearest the earth. Mercury, 

Venus, Mars. 

3. What keeps bodies on the surface of the earth? Gravity. 

4. A\'hat changes are caused by the revolution of the earth 

around the sun? Change of seasons. 

5. What instrument do mariners use to determine direction? 

Compass. 

6. Latitude is measured on what lines? Meridians. 

7. The great highlands of the continents form a great horse- 

shoe from where to where? Cape Horn to Good 
Hope. 

8. Which planet has four moons? Jupiter. 
Q. Which planet has the rings? Saturn. 

10. How have mountains been formed? By the folding of 

the rock layer. 

11. What term is applied to the wearing away of the land? 

Erosion. 

12. Give the most noted example of erosion in Carbon 

Coimty. Lehigh Gap. 

13. What is the inclination of the earth's axis? 23 1-2 de- 

grees. 

14. H the earth inclined 33 1-2 degrees what would the width 

of the temperate zone be? 23 degrees. 

15. What is the name of the path in which the earth travels 

around the sun? Orbit. 

16. The Frigid Zone is cold because the sun's rays fall how? 

Slanting. 

17. What is wind and how caused? Air in motion caused 

by its unequal heating. 



9 

i8. What usually causes deserts? Alountains or lack of 
them. 

19. Give the scientific name for the black race. Ethiopian. 

20. What prevents the possibility of boiling egg's on the sum- 

mits of the highest mountains? Atmospheric pres- 
sure. 

21. What barrier causes the fauna of Australia to differ from 

the rest of the world? The ocean. 

With the eighth grade each repetition was conducted orally 
during the various parts of the day indicated. This would 
give the individuals that were not reciting an opportunity to 
hear 17 repetitions; since, however, individuals were called 
upon at irregular periods of the day such as suited the con- 
venience of the teacher or pupil, it is probable the attention 
of each pupil was concentrated on some personal and individ- 
ual task, and that not nearly seventeen repetitions were heard 
by any one pupil. 

In conducting this experiment such disposal of the diffi- 
culties that presented themselves was made as the exigencies of 
the case seemed to warrant. The results are reliable only 
to the extent of being reasonably approximate. Among the 
factors which prevented the experiment from being scientifi- 
cally accurate are the following: 

1. The number of individuals with whom the experi- 
ment was tried was too small. The experiment should be 
tried with a large number of pupils, several thousand. 

2. The number of slow learners varied in several of the 
groups and would proportionately modify the showing of the 
group. 

3. The period during which the experiment was con- 
ducted was entirely too short to conclude that the facts pre- 
sented and repeated were fixed with maximum certainty of 
permanent recall. It took but a very short time until the facts 
were fixed, but the term's close was too near to allow the 
interval between the various repetitions to be constantly in- 
creased. 

4. The number of repetitions was modified by some of 
the children using them after the fourth repetition in their 
playing school. The brighter children of the fifth grade 
could repeat the questions and answers after the fourth repe- 
tition, and used them in the hall as lesson for their play school. 
Individuals of the other grades also were observed to ask 
the questions at random of each other. 

5. The facts should always be presented by the same 
individual so there could be associated with each individual 
fact the same bits of interesting detail that would make all 
the facts equally well remembered by each group of children 
and each fact equally as fully apperceived. 

6. The desire and anxiety on the part of some of the 



10 
teachers whose children were experimented upon to have the 
results appear well may have caused them to give hints during 
the repetitions that slightly modified the results. 

7. In several cases the word required for the answer 
was correctly retained, but the content which the presenter 
had hoped to connect with it permanently could not be even 
reproduced in part, and was probably entirely forgotten. 

8. Answers were received that were substitutes for the 
ones required, and from these answers it was impossible to 
determine whether the child had the presentation that was 
given, or whether apperception had made such contributions 
and association had caused such related ideas to function that 
the content in the learner's mind no longer corresponded to 
that at the close of the original presentation. 

In an examinaion of the fifth and sixth year folks that 
was given at the end of the school year, in answer to the gen- 
eral question, "Tell all you can of South America," "of Aus- 
tralia ;" each individual included in his answer some of the 
facts that were presented in the experiment. One individual, 
a fifth grade pupil, included eighty-one per cent., and no in- 
dividual had less than twenty per cent. 

The question relating to the formation of the Australian 
Federation, the date 1908 was substituted for the one re- 
(|uired by two individuals on three different repetitions. 

In the case of questions that were so framed as to re- 
((uire two or more words for an answer, during the earlier 
repetitions, it happened that only part of the required answer 
was recallable ; this same thing did not occur during the later 
repetitions, due possibly to the fact that the associations be- 
tween the various parts of the answer became more perma- 
nent as the result of the oral repetitions of the errors that 
were made during the written repetition. 

By an examination of the sheets containing the results if 
will be seen that the fifth grade folks practically knew the 
twenty questions at the end of the fourth repetition, the sixth 
year folks by the end of the fifth repetition, the seventh year 
folks by the end of the fourth repetition, and the eighth 
year folks by the end of the third repetition. Averaging these 
approximations the statement might be made that the twenty 
facts were learned with four repetitions. 

That the outcome of the experiment should be as it is, 
surprises no one more than myself. Though these results 
lack absolute exactness, they are sufficiently exact to give 
us the information necessary to direct intelligently our future 
educational method, and aid us in the intelligent selection of 
our education content. It is accurate in a sufficient degree 
to indicate to us the kind of method that should be used 
to fix essential content. The essential feature of this method 
must be, not several repetitions in a short period of time; 



11 

but a relatively small number of repetitions with a constantly 
increasing interval of time betvi^een the repetitions that con- 
tinue through rather a long period. 

In the results which follow, the numbers along the left 
liand side of the column of figures indicate the number of 
pupils. Absences are indicated with a cross. The numbers 
below the repetitions, as indicated at the top of the columns, 
denote the number of errors that were made by the various 
individuals. The date at the top of each column means that 
the repetition was conducted upon that day. 



12 
Results with Fifth (irade 



I 


5 


3 


























2 


3 


3 


2 


1 





I 














3 


5 


2 


I 























4 


2 








I 




















5 


6 


4 


3 


2 








I 











6 


7 


2 


5 


3 


I 

















7 


8 


4 


3 








2 


I 











8 


4 


I 


2 





I 











I 





9 


5 


3 


























lO 


3 


2 


























11 


5 


3 





I 








I 











12 


3 


5 


2 


1-3 




















13 


6 


2 








1-3 

















14 


3 


2 


























15 


5 


4 





I 








1-3 











16 


I 





























17 


4 


2 





1 




















18 


7 




4 


2 


2 





I 











19 


2 








I 




















20 


4 


3 


2 


r 





I 








I 





21 


6 


2 


























22 


5 




2 


I 


I 

















23 


3 











. 

















24 


5 


4 


I 














1 








25 


6 


I 











I 








2-3 





26 


7 


2 








1-3 

















27 


4 


4 


4 


3 


I 








I 








28 


9 


7 


6 


4 


2 





2 


r 








29 


7 


5 


3 





I 

















30 


6t 


-3 3 





I 




















31 


H 


12 


7 




4 


3 














32 


7 


4 


2 





5 


1 











I 


33 


6 


3 


























34 


12 


4 


3 








2 





I 








35 


3 


4 


2 


I 





I 














3^> 


7 


2 


2 





I 











I 





2^7 


6 


4 T 


-30 


2 




















3^ 


T 





























?<') 


3 





I 























40 


I 








I 





















13 

Kesults with Sixth (Jrade 



I 


4 


3 


2 


I 




















2 


3 


4 





I 


I 


I 














3 


3 


I 





3 


3 


2 














4 


7 


5 





4 


2 








I 








5 


4 


3 


2 























6 


6 


2 


3 





2 








r 








7 


6 


3 


2 























8 
































9 


5 


2 


1 





2 

















lO 


8 


4 


4 


I 


2 


I 













II 


5 


5 


3 


3 


2 





2 











12 


3 


2 


I 


I 


I 











I 





13 


5 


4 


3 








I 













14 


6 


3 


2 


I 













I 





15 


2 


I 


























16 


4 


2 











4 





I 








17 


8 


5 


3 


2 





I 














1 8 


5 


3 


I 























19 





2 


3 























20 


3 





I 























21 


6 


3 


2 


I 


I 








I 








22 


2 


I 


























23 


4 


2 


I 























24 


8 


5 


3 


2 


I 


I 





I 


I 





25 


5 


3 


I 


I 




















26 


3 


2 


























27 


3 





























28 


5 


4 




4 


3 


2 


I 











2(; 


6 


5 


4 


3 


2 






. . 






30 


10 


7 


6 


4 


2 


1 





I 








31 


3 


4 


8 


4 


I 


2 








I 






14 
Results with Seventh Grade 



I 


7 


3 




















2 


5 


4 


2 

















3 


4 























4 


























5 


5 


3 





I 














6 


5 


5 


4 


2 





2 


I 


I 


7 


14 


6 


5 


3 





I 





2 


8 


3 





2 


I 














9 


5 


4 


3 











1 





lO 


3 





2 


I 














II 


4 





2 

















12 


2 























13 


























U 


7 


4 


3 








I 








15 


16 


13 


7 


4 





2 


I 




16 


16 





4 


2 





2 








17 


13 


5 


2 
















18 


4 


2 




















19 


18 


12 


5 


I 





3 


2 


I 


20 


3 























21 


5 


2 














I 





22 


8 


3 





I 





1-3 








23 


5 





2 








2 








24 


6 


4 


3 











I 





25 


8 


6 


4 


3 














26 


3 


I 




















27 


I 























28 


9 


4 


3 


2 








3 





29 


13 


7 


4 


2 





2 


3 





30 


4 





2 


I 















15 
Results with Eighth Grade 



1 


2 


I 




















2 


2 


I 




















3 


4 


I 


2 


I 














4 


I 























5 


5 


3 


2 


I 













6 


2 























7 


3 


I 


2 


I 














8 


I 


2 


I 

















9 


I 























lO 


2 























II 


3 


2 




















12 


I 























13 


6 


4 


3 

















u 


I 























15 


4 


2 



















16 


2 


I 




















17 


1 














n 








18 


3 


2 


2 


















IG 

THE SECOND EXPERIMENT. 

The facts which are asked for in the following- questions 

are the ones that were used in the experiment to determine 

the number of repetitions that would be necessary to fix them 

with maximum certainty : 

1. What is the area of your county? About 400 square 

miles. 

2. Where was it first settled? At Lehighton. 

3. What five persons are conspicuously connected with its 

settlement? White, Hazard, Hauto, Hillegas and 
Cist. 

4. What nickname was applied to Robert E. Lee's father? 

Light Horse Harry, 

5. How many feet above sea level is the highest point of 

your county? 1735 feet. 

6. What is the meaning of the Indian name Towamensing? 

Wilderness. 

7. What five persons are connected with the walking pur- 

chase? Edward Marshall, James Yeats, Solomon 
Jennings, John Penn and Tom Penn. 

8. What was the most important sentence uttered by Pat- 

rick Henry in the Congress at Philadelphia which 
he attended? "I am not Virginian, but an American." 
(). What was the value of the most important commercial 
product produced in your locality in 1907? Coal, 
$9,000,000. 

10. What is commercially the most important river in the 

world? The Chicago. 

11. Name the five largest cities of the United States with 

their approximate population. New York, 4 mil- 
lions ; Chicago, 2 millions ; Philadelphia, i million ; 
Boston. 649 thousand; St. Louis, 602 thousand. 

12. What did Paul Revere say to the men who were guard- 

ing the house in which Plancock and Adams were 
sleeping? "Noise! You'll soon hear noise enough, 
the Regulars are coming." 

13. How many men were lost by the British and the Ameri- 

cans at the battle of Lexington? Americans 93, Brit- 
ish 2'J2^^ 

14. What five geological strata have their outcrop in your 

locality? Pottsville Conglomerate, Pocono Sand 
Stone, Mauch Chunk Red Shale, Coal Measures, 
Oriskany Sand Stone. 

15. Name one of the two important political institutions be- 

gun in \^irginia in 1619. Slavery or representative 
government. 

16. What did Lincoln say when he heard of the capture of 

Vicksburg? "The father of waters now rolls un- 
vexed to the sea." 



17 

ly. About how many men did the United States lose by the 

Civil War? About 500,000. 
18. What is the name that is applied to the plant from which 
a large part of the coal was formed? Lepidoden- 
dron. 
IQ. Name five men from Pennsylvania who signed the Decla- 
ration of Independence. Robert Morris, Benjamin 
Franklin, Benjamin Rush, James Wilson, James 
Smith, George Ross, George Taylor and Morton 
Clymer. 
20. What were the last words of Stonewall Jackson? "Let 
us cross over the river and lie down under the shade 
of the trees." 
In the light of the results obtained in the experiment of 
the year before, it seemed advisable to continue the work of 
this year along the same general line, but under somewhat 
different conditions. Whereas, in the previous experiment 
all known available means were used to make the first pres- 
entation eft'ective in a maximum degree, in this investigation 
no attempt at emphasis or explanation of any kind was made. 
The facts to be learned in the second experiment were very 
much more numerous than in the first, less likely to be easily 
associated with any facts which the children already knew, 
and much more likely to contain difficulties of comorehension 
and understanding. Especially unrelatei to anything in the 
children's experience were the facts called for in question 
number fourteen. Much of what children are required to 
learn in sclv^ol is like Greek to them, and it was deemed advis- 
al:lc 1 V the members of tlie Seminar to determine how the 
learning of such facts as to them have nrobablv no meaning 
or Init little meaninp-, compared with the learning of facts such 
as are readily associated by them or were made associable by 
the exoerinienter. Tn the first experinient care was taken to 
select only such facts as seemed essential or would be taught 
as part of the regular content of the year. In the second in- 
vestigation an attempt was made to have the facts as hetero- 
geneous as possible and as numerous as could be repeated dur- 
ing one continuous period of mental effort. In the first ex- 
periment the facts were relatively few and presented in the 
most effective manner known, in connection with the regular 
work of the class in the subject to which they belonged ; in 
the second thev are quite heterogeneous, as numerous as pos- 
sible, almost nonsense syllables in many cases, and presented 
without instruction or explanation. 

The questions numbered i. 5, 0. 17. require one number 
for an answer, while i.^ requires two. The questions num- 
bered 2, 6. TO and t8 are answered with one word as also is 
number t^. Nmnbers ^ and 7 require the names of five in- 
dividuals, but number T i needs for its answer the names of 



IS 
five cities with which it was supposed that each child in- 
cluded in the test was fairly familiar, and after the names of 
these cities he was required to write the numbers which repre- 
sented their approximate population. Three of these numbers 
he was requested to write by prefixing the figures 4, 2 and i 
before the word million, and the other two of the five num- 
bers required to answer question number 11. it was necessary 
for him to write 649 and 602 before the word thousands. Ques- 
tion number 14 is answered by five terms all of which were 
new to the children, rather difficult to spell, and about as diffi- 
cult to remember for most of the children as nonsense sylla- 
bles usually are. As an answer for question number 19, the 
five names of five signers of the Declaration of Independence 
which were placed first in the list were most frequently writ- 
ten. With at least three of these all of the children in the test 
were familiar, and it is quite probable that the children had 
met all of the names at some time during their school careers. 
Every time that the answer for number 19 was repeated the 
names of the eight men were repeated, but the children were 
never required to write more than five. 

Question number 4, though grouped with the quotations, 
is in fact only a nick name of three words and each of these 
is easily remembered. The answer to questions number 8, 
12, 16 and 20, is a short cfuotation associable with facts 
with which the children are already fairly familiar, but is the 
expression of an- idea in a form that was entirely new. The 
general nature of the questions may be readily seen from the 
following summary : 

Numbers i, 5, 9, 13, 17 are answered by a figure. 

Numbers 2, 6. 10, 15. 18 are answered by one word. 

Numl:)ers 3, 7, 11, 14, 19 are answered by five words. 

Numbers 4. 8. 12, 16. 20 are answered by a quotation. 

The directions which were given to the various teachers 
for conducting the experiment were as follows : 

1. The teacher will read the first question. 

2. The teacher will read the answer to the first question. 

3. The pupils will write the answer to the first question 
on slips of paper prepared for the purpose. 

4. The teacher will read the second question. 

5. The teacher will read the answer to the second ques- 
tion. 

6. The pupils will write the answer to the second ques- 
tion. 

7. The teacher will read the third question. 

8. The teacher will read the answer to the third question. 

9. The pupil will write the answer to the third question. 

10. Thus the teacher will continue to read the (juestions 
and then the answers, and the pupils will thus continue to write 
the answers until all the (juestions and answers have been 



19 
read and all the answers have been written. The papers will 
then always be sent to the principal. 

11. The teacher will then collect the papers on which 
the answers were written and send them to the principal. 

12. At all later repetitions the teacher will read the ques- 
tions only, but always in the order in which they are number- 
ed. The pupils will write the answer to each question imme- 
diately after it has been read. 

13. Thus they will continue until the facts are learned; 
the principal will always fix the date at which a repetition of 
tlie facts is to be made. 

14. At the close of each repetition, after the papers have 
been collected the teachers will again read the question and 
answers in such a way that the reading of each question will 
be followed by the reading of the answer in regular succession. 

The directions were given in this form in the hope of 
securing uniformity. To have each child write the answer as 
it was presented to him immediately after the first question 
was read at the first presentation gave all an equal opportunity 
to get the impression clearly, and by writing it there was 
maximum certainty that the impression was received correct- 
ly. When the answer that was required had once been defi- 
nitely fixed, the likelihood was that each following repetition 
would bring the response required. Oral repetition was prac- 
tically impossible because of the time it would have required. 
It was deemed wise to repeat the correct answer to each of 
the (|uestions immediately after the children had maae an 
attempt to answer them, since it was supposed that each child 
would listen with close attention for the answers which he 
was conscious of having missed. Re])eating the questions and 
answers after each repetition had the advantage of making 
the repetition uniform for each individual of the group, absent 
ones, however excepted. ( )n the sheets containing the results 
absentees are indicated by an addition sign. 

It is impossible to determine just how faithfully the direc- 
tions were followed. In the high school the experimenter him- 
self was present at each repetition, and the probability is that 
the results on the high school sheet represent the honest efifort 
of the group during the time the experiment was in progress 
according to the directions as given. Just how to account for 
such phenomenal improvements as a drop from twenty-eight 
errors to five, or from thirty to one as is indicated in numbers 
18 and 19, is rather perplexing. That it may have been possible 
for these individuals to have made a copy of the answers as 
they were being repeated by the experimenter, is true, but not 
likely. Especial vigilance on the part of the three teachers in 
the room at the time would probably have detected the indi- 
viduals writing had any of them attempted it. The individuals 
are apt learners and it is my belief that they simply remem- 



20 
berecl the facts. 

The intervals between the rei^etitions were by no means 
uniform. As stated before, the lirst experiment conducted 
in connection with work the Pedagogical Seminar had to do 
with the learning of facts that would ordinarily occur in con- 
nection with the regular school work under ordinary normal 
school conditions as nearly as possible. The second differed 
from the first in that the facts to be learned were much more 
numerous and had but little connection with the regular school 
work, and were presented without any attempt to make the 
presentation as effective as possible. 

In the results that follow, the number of pupils, the num- 
ber of errors and the date of the repetition is indicated as in 
the first experiment. The record marked Sixth and Seventh 
grade was made by a group of chidren in these grades that 
were targht in the same room by the same teacher. Those 
marked A Grammar represent the results of the eft'orts of the 
eighth grade pupils, while those marked Hauto were made by 
the grades indicated, all being taught in the sa;iie room by one 
teacher. 

The result sheets for the high school and the seventh 
grade explain themselves, since all the factors recorded are 
indicated just as on the previous result sheets. The sheet 
marked Sunimary of Errors is a tabulation of the errors that 
were made by the various groups whose record in the second 
experiment have preceded. The numbers and letters in the 
left hand column indicate the number and part of the various 
questions. The numbers in the succeeding columns tell how 
many errors were made by the groups in answering that par- 
ticular qrestion whose number is indicated by the figures in 
the left hand column. The respective groups and the number 
of pupils that were in each is indicated at the top of each 
column. The number in the right hand column indicates the 
number of errors that were made in answering the questions 
indicated by the entire group. On the sheet marked "Facts 
Arranged according to Number of Errors" the figure in the 
first column indicates the number of the question, the number 
in the second column the entire number of errors that were 
made with the particular question, and in the third column 
are the answers desired, or a word describing the answer that 
was exepected to be given. 

On averaging the number of repetitions that were re 
(|uired to learn the facts by tlie various individuals the follow- 
ing facts ap])eared : 

Average numlier of repetitions requirerl by high school 
])upils 6. 

Average numlier of rejietitions required 1)v sixth and 
seventh grade 7.5. 

Average number of repetitions required by seventh grade 



21 

7-5- 

Average number of repetitions required by A Grammar 
grade 6. 

Average number of repetitions required by Hauto Pupils 
6. 

The conclusion would, from this, be justifiable that the 
facts were learned in about seven repetitions. 



22 
HIGH SCHOOL 



I 


32 


15 


5 





2 


4 


3 


3 







2 


32 






17 


13 


II 






4 


6 9 


3 


32 


22 


23 


15 


19 


18 




17 


13 


3 5 


4 




29 


17 






18 








. . 










5 


23 


15 


8 


3 


4 


6 


5 


4 


4 


4 •• 


6 




14 


8 


7 


II 




14 




II 


I 


7 


31 


13 


6 


3 














8 




13 


7 


7 


5 


11 


9 


3 


4 





9 


17 


I 


I 



















lO 


16 


I 























II 


18 


2 


2 




4 













12 


18 


II 


2 









I 








13 




3 








I 





' 








14 


24 

























15 


19 


7 


I 



















16 




16 


7 




4 













17 




20 


15 


9 


II 


16 


9 


8 


3 





18 


28 


5 























19 


30 


I 























20 


23 

























21 


18 






2 


"s 


4 


2 








22 


5 


I 








I 


I 


I 








23 


13 


8 


2 




















24 


27 


6 





I 




I 











25 


31 


13 


5 


2 






2 








26 


13 























27 


31 


17 


'6 


I 


1 


I 











28 


12 


























29 




15 


19 


I 


3 


I 


2 








30 


31 




19 


4 


I 














31 


17 












4 


I 








32 


31 










3 











33 


29 


22 


9 





8 


5 


4 


2 






34 


V 


28 


15 


9 


4 


4 


2 






. 


35 




II 


12 




5 


6 


6 


2 






36 


29 


16 


10 


6 


4 


3 


4 


I 






Z7 


10 


3 









4 


2 








38 


22 


I 


I 











2 








39 


24 










2 




5 


I 




40 


34 


15 


9 


2 


6 


7 


5 




I 




41 


29 


16 


14 


9 


9 


II 


4 


5 


I 




42 




23 


7 




10 


13 


3 


2 







23 

A GRAMMAR 



I 


15 


15 


10 


I 






14 


2 


13 


6 


2 


8 


II 


8 




3 


7 


2 






9 




15 


4 


2 


I 








3 


3 





5 


15 


2 










5 





6 




34 


18 




u 


14 


I 


7 


22 


3 


2 




3 







8 


4 


5 

















9 


20 


7 








2 


I 




10 


15 


5 


I 








I 




II 


17 


8 


2 


3 


2 







12 


7 


1 






6 


3 




13 


II 


3 
















14 


3 













2 




15 


4 


I 
















16 


14 




2 


I 





I 




17 


19 


'8 










2 


18 


II 


9 


2 


I 


3 




2 


19 


20 


19 




7 


II 


6 


I 


20 


26 


14 


5 


3 


II 


5 


2 


21 


i.^ 


I 











4 


2 


22 


9 


2 


2 





I 


3 






HAUTO. 5ili 6th 7th 



3 
Cu 


^ 














S 


I 


6 


19 


15 


15 


8 


10 


8 


2 


2 


16 


9 





2 











3 


8 


10 


I 


I 




2 







4 


8 








I 














5 


22 


21 


5 


9 




I 





14 


6 


21 


6 


14 


8 


'8 











7 


9 


14 


5 











I 





8 


7 


2 


I 


2 














9 


4 

















I 


4 


10 


7 








I 





I 








II 


15 








I 


I 










12 


5 


2 

















I 


13 


15 
















I 




14 


12 


8 




I 





2 










18 


17 


II 


II 


5 


6 


10 


5 


16 


19 


9 





2 











I 


17 


14 


10 








2 









18 


31 


29 


29 


9 




5 


5 




19 


18 


3 


8 


I 





2 








20 


24 


22 


19 


16 




6 


5 


7 


21 


8 


I 

















22 


19 


10 


6 


5 


"8 


6 


5 


7 


23 


6 


3 



















24 


14 


16 


II 


15 


12 


10 


'8 


12 


2S 


5 


I 








I 











26 


9 


17 


I 


10 


4 


I 





I 


27 


14 


2 


3 


7 


I 





2 





28 


14 


17 





2 


5 


3 




2 



24 

Sixth and Seventh Grade 



I 


24 


15 


7 


2 


8 


7 


8 







2 


36 


15 


14 


14 


7 


15 


8 


II 


I 


3 


18 


6 


5 


3 




5 


9 


3 


2 


4 


27 


II 


7 


5 


5 


18 


9 







5 


12 


6 


8 


6 


9 




5 







6 


38 


27 


29 


24 


29 


36 


Z^ 


33 


33 


7 


32 


15 


12 


10 


8 


15 


12 


7 


4 


8 


35 


20 


9 




15 


12 




9 




9 


31 


II 


9 


6 


19 




10 


5 


9 


10 


27 


10 


7 


5 


8 


13 


10 


5 




II 


26 


II 


5 


7 












12 


24 


6 











3 









13 


28 


4 


6 


5 


2 


3 









14 


27 




3 


8 


7 


5 


2 






15 


26 


5 


5 


3 


4 


3 


2 






1 6 


15 


3 


2 

















17 


18 


I 





















i8 


14 














2 








19 


14 


3 


2 








5 


I 






20 


21 


3 


5 


3 


3 


2 








21 


24 


3 


3 


2 


3 


2 








22 


14 














2 








23 


14 


5 


I 








I 








24 


12 


7 


4 








18 


12 





25 


36 


26 


29 


^6 


20 


25 


7 




I 


26 


22 


13 






5 


5 


10 


4 





27 


3 





I 





4 








2 




28 


25 


8 





2 





7 


3 


I 




29 


23 


7 


4 


2 


2 


4 


7 


2 





25 

Seventh Grade 



I 


27 


19 


15 




8 


13 


13 




10 


5 


2 


27 


20 


19 


20 


10 


15 


18 


6 


9 


4 


3 


24 






26 


2 












4 


27 


17 


12 


12 




15 


4 


9 


3 





5 


27 


25 


16 


21 


3 


4 


10 


5 


I 




6 


28 


23 


17 


20 


5 


10 


9 


7 


6 


I 


7 


29 


20 


15 


17 


9 


10 






4 


I 


8 


29 


26 


22 


24 


I 




12 


3 




I 


9 


34 


28 


14 


17 


8 


3 


I 








10 




28 


19 




5 


12 


2 








II 












. . 


I 









12 


26 


18 


8 


9 





10 


I 








13 


37 


30 


19 


23 


7 


8 


2 








14 




5 


2 


I 






I 








15 


20 


9 


7 


















16 


28 


16 


18 


25 


I 













17 




6 


7 


5 





I 










18 




18 


14 




I 


7 











19 


24 


14 


6 


10 


9 


8 


I 








20 




27 


24 




8 


19 


15 









21 


27 


22 


21 


20 


8 


12 


4 


2 






22 


27 


18 


19 




4 


9 


6 









23 


34 




24 


21 


6 


8 


8 









24 


25 


17 


10 


II 


2 


12 


7 









25 


22 


II 


7 


9 





8 


5 









26 


30 


19 


15 




II 


II 




I 






27 


28 


20 


12 


13 


2 




12 




6 


2 


28 


32 


20 


25 


20 


6 


15 


8 


I 






29 


28 


22 


15 






6 




13 







30 


28 


25 


14 


19 


2 


9 




7 







31 




21 


II 


17 


4 


6 


s 


4 


I 




32 


27 


21 


14 


13 


5 


15 


6 


6 


2 




33 


29 


15 


9 




44 


6 


8 


6 







34 


25 


20 


18 


16 


9 


16 


7 


'■ 


2 




35 


29 


16 


15 


12 


4 


II 


11 


5 







36 


26 


14 


13 


13 


26 


12 


8 


3 







37 


38 


27 


26 


25 


7 


20 


12 


7 


I 




38 


33 


28 


19 






16 


12 


18 


2 




39 


30 


27 


18 


30 


7 


13 


8 


7 


2 





26 
Summary of Errors 





3 
£ a- 


d-' 


^.^ 


t^ 3 


■ 3 
0^ 


CO "- 






= <M 


_ O) 


•£ av 




^ ^ 


. 






X 4= 


Oa ro 


CO ro 


CO f^ 


< (M 


ID ro 




I 


8 


12 


8 


5 


4 


I 


38 


2 


14 


39 


15 


4 


5 


I 


78 


3a 


20 


51 


6 


24 


10 


4 


115 


b 


38 


83 


21 


29 


17 


2 


190 


c 


44 


108 


27 


34 


II 


4 


227 


d 


56 


III 


40 


64 


21 


6 


288 


e 


59 


80 


41 


66 


17 


9 


272 


4 


7 


II 


4 








I 


23 


5 


46 


75 


13 


46 


7 


6 


193 


6 


14 


17 


3 


II 


2 


2 


49 


7a 


47 


96 


55 


43 


17 


13 


271 


b 


57 


no 


81 


51 


18 


17 


334 


c 


55 


128 


100 


64 


32 


18 


377 


d 


59 


146 


82 


59 


31 


20 


317 


e 


60 


107 


58 


57 


32 


27 


341 


8 


8 


21 


14 


10 


16 


8 


76 


9 


22 


50 


42 


30 


6 


44 


194 


10 


5 


4 


7 


12 


3 


5 


36 


iia 


35 


79 


52 


30 


9 


13 


218 


b 


63 


123 


87 


42 


19 


26 


360 


c 


68 


133 


7Z 


44 


23 


34 


375 


. d 


77 


190 


136 


72 


28 


43 


546 


e 


98 


166 


125 


72 


39 


45 


545 


12 


13 


II 


5 


4 


5 


10 


48 


13a 


33 


26 


5 


13 


7 


12 


96 


b 


51 


47 


32 


21 


33 


26 


210 


14a 


43 


49 


46 


16 


6 


41' 


201 


b 


66 


91 


68 


19 


16 


52 


312 


c 


72 


115 


65 


34 


II 


62 


359 


d 


85 


127 


76 


52 


14 


74 


428 


e 


84 


108 


64 


58 


22 


77 


413 


15 


56 


14 


42 


28 


5 


12 


157 


16 


32 


52 


56 


30 


25 


35 


230 


17 


67 


122 


93 


34 


26 


34 


384 


18 


40 


7^ 


63 


34 


5 


10 


224 


19a 


35 


90 


62 


33 


21 


35 


276 


b 


47 


136 


87 


43 


23 


40 


376 


c 


60 


136 


98 


68 


29 


37 


398 


d 


77 


157 


109 


74 


40 


56 


513 


e 


74 


125 


82 


75 


41 


59 


456 


20 


15 


23 


16 


12 


4 


15 


95 



27 

Facts arranged according to nunaber of errors 



4 ■ 


23 


Nickname. 




lO 


36 


Chicag-Q. 




I 


38 


One Number. 




12 


48 


One Number. 




6 


49 


Wilderness. 




8 


76 


Quotation. 




2 


78 


Familiar Name. 




20 


95 


Quotation. 




13a 


96 


Number. 




3a 


"5 


Packer (town). 




15 


157 


Slavery or Rep. Gov. 




3b 


190 


Hauto(town). 




5 


193 


Number. 




9 


194 


Number. 




14a 


201 


Potts. Cong. (town). 




13b 


210 


Number. 




iia 


218 


City & Number. 




18 


224 


Term (Rhododendron). 




13c 


227 


Hazard (Town). 




16 


230 


Quotation. 




7a 


271 


Marshall (unfamiliar name). 




3e 


272 


Cist (unfamiliar name). 




19a 


276 


Robert Morris. 




3d 


288 


Hillegas (unfamiliar name). 




14b 


312 


Pocono Sandstone. 




/b 


334 


James Yeats (unfamiliar name). 




/e 


341 


Solomon Jennings (unfamiliar name) 


14c 


359 


Mauch Chunk Red Shale. 




lib 


360 


Chicago, 2 mill. 




19b 


376 


P>enjamin Rush. 




lie 


375 


Phila.. I mill. 




17 


384 


500,000. 




7d 


397 


John Penn. 




19c 


398 


Franklin. 




/c 


399 


Solomon Jennings. 




14c 


413 


Oriskany Sandstone. 




i4d 


428 


Coal Measurer (familiar). 




196 


456 


James Smith. 




i9d 


513 


Morton Clymer. 




lie 


545 


St. Louis, 649 thous. 




iid 


546 


Boston, 602 thous. 





28 
THE THIRD EXPERIMENT. 

In the light of the results obtained in the previous exper- 
iments, it seemed advisable to try to determine how the learn- 
ing of forgotten facts compared with the results in former 
experiments. In order to make this comparison, the following 
list of questions was selected to be used with the pupils in the 
high school. All the children now in this school were taught 
in the A Grammar room by the same teacher. He declares 
that every pupil who passed through his room at one time 
knew the facts called for in the questions. 

The experiment was conducted by the experimenter in 
accordance with the directions given for the second experiment, 
except that there was no first presentation of the facts. It 
was assumed that each pupil was familiar with the facts and 
the first exercise of this experiment was conducted just as 
was the first repetition in the first and second experiment. The 
interval was arbitrarily fixed at a week, though the results 
would no doubt have been somewhat better had the interval 
been shorter. The number of questions was so arranged as 
to require the writing of about as many facts as were required 
in the second experiment. This, it was thought would make 
the matter of comparison somewhat simpler. The questions 
used follow : 

I. I. How many degrees from the north pole to the 
equator ? 90. 

2. In what year was the ordinance passed which re- 
lated to the government of the Northwest Territory? 
1787. 

3. In what year was Jamestown settled? 1(J09 

4. When was the Pacific Ocean discovered? 15 13. 

5. In what year was the Mexican War begun? 1848. 
II. I. In whose administration did the President refuse 

to sign the Bank Charter? Jackson's. 

2. In whose administration was Louisiana purchased? 
Jefiferson's. 

3. In whose administration was the Second War 
with England? Madison's. 

4. In what war was the Battle of Long Island fought ? 
Revolutionary. 

5. To what party did Thomas Jefiferson belong? 
Anti Federalists. 

III. I. What large islanrl south east of Africa? Madagas- 
car. 

2. What ocean south of Hindoostan? Indian. 

3. What mountain range between Europe and Asia? 
Ural. 

4. What river between the L^nited States and Canada? 
St. Lawrence. 

5. What cape at the southern extermity of South 
America? Cape Horn. 



29 

IV. I. By whom was South America discovered? Colum- 

bus. 

•2. Who probably was the originator of the Monroe 

Doctrine? J. Q. Adams. 

3. By what title is the ruler of Turkey known? 
Sultan. 

4. How many years did Washington serve as Pres- 
ident ? Eight. 

5. What leader crushed the Creeks and Seminoles 
in Florida? Jackson. 

V. I. Name in their order five rebellions that have occur- 

red in our history, (a) Claybourne's, (b) Bacon's, 
(c) Whiskey, (d) Dorr, (e) Great Rebellion. 
VI. For what achievement are the following men noted? 

1. Thomas A. Edison. 

2. S. F. B. Morse. 

3. Geo. B. Meade. 

4. Eli Whitney. 

5. Elias Howe. 

MI. Beginning with Florida name five States in succession 
that border on the Atlantic Ocean, Florida. Georgia, 
South Carolina. North Carolina and Virginia. 
VIII. I. What is the capital of Germany? Berlin. 

2. What is the capital of Cuba? FEavana. 

3. In what country is Sydney located? New South 
Wales. 

4. In what country is Buenos Ayres located ? Argen- 
tine Republic. 

5. In what country is Venice located? Italy. 

IX. State briefly the sutstance of the Monroe Doctrine. 

For any Euronean country to try to gain dominion 
in America will be considered an unfriendly act by 
the United States. 

Of the forty-one possible errors the best record was made 
by a boy who wrote all of the answers correctly except seven, 
and the poorest record was made by a girl who missed thirty- 
six. No one was more surprised than the experimenter to 
learn that so many of the facts once well known and quite 
familiar should so soon be forgotten. The teacher who taught 
the pupils while they were in the Grammar School was equally 
surprised. 

Thirty of the individuals in the test learned to write the 
forty-one facts by having two repetitions ; the remaining thir- 
teen required three. The ease and readiness with which they 
were recalled is perhaps as surprising as the fact that so large 
a part of the educational content, which was considered well 
taught and well known, should have been so easily forgotten. 

In the results which follow, the numbers in the first col- 
umn denote the number of pupils and the other numbers indi- 
cate the errors made in the various repetitions. With the pu- 
pils after whose number there is nothing in the third column 
the facts were learned in two repetitions. 



30 
Fifth Grade Facts of Experiment 



1 8 

2 71-3 


41 
II 


-3 



61 



-3 


3 12 1-3 

4 17 

5 82-3 

6 62-3 


32 

7 

51 

I 


-3 
-2 


4 

5 


I 


I 

32-3 

I 

2 


7 91-3 

8 82-3 


4 

I 




I 




2 



9 81-3 













10 10 1-3 


2 










1 1 8 2-3 













12 62-3 







1-2 





13 13 1-2 

14 12 1-2 


22 
2 


-3 


4 

I 


5 



15 65-6 


I 










16 12 1-3 







I 


I 


17 14 1-2 

18 13 1-3 








41 

I 


-3 3 

I 


19 12 

20 12 1-3 


5 
6 




2-3 

7 


2 
6 


21 61-3 







2 





22 14 2-3 


I 




2 I 


-3 


23 91-2 







3 





24 20 

25 13 1-3 

26 8 


7 






7 
I 



41-3 
1-3 


27 19 

28 142-3 

29 16 

30 13 1-3 

31 172-3 

32 6 2-3 


9 1- 


I 
6 
8 



-3 


11 
81 
3 

5 
12 

I 


102-3 

-3 3 
I 
I 

61-3 
2 


33 15 

34 16 

35 17 
416 1-2 1 




2 I 


905- 


-3 
-6 


I 

4 
1-2 
98 



3 
4 
631-3 



31 

Results of Repetition of Facts Used in 

Third Experiment 



o 



2 


c 




I 


12 


10 


4 


2 


II 


10 


13 


3 


4 


9 




4 


13 


6 


I 


5 


9 


7 





6 


5 


5 


I 


7 


15 






8 


13 


I 





9 


20 


13 




lO 


10 


4 


I 


II 


II 


5 


2 


12 


5 


7 


I 


13 


13 


6 


18 


14 


7 


6 


2 


15 


4 


2 


I 


i6 


8 


10 


9 


I? 


4 


2 





i8 


15 


7 


2 


19 


14 


14 


17 


20 


16 


II 


12 


21 


5 


4 





22 


9 


4 


5 


23 


10 


13 


12 


24 


10 


I 


2 


25 


7 


I 





26 


10 


12 


4 


27 


10 


II 


13 


28 


9 


4 




29 


13 


I 


'6 


30 


9 


7 




31 


5 


7 


5 


32 


8 


I 


I 


33 


5 


4 





34 


9 


3 


5 


35 


9 


8 


II 


36 


15 


15 




37 


8 


14 


's 


38 


3 








39 


8 


7 




40 




20 


12 


41 


14 


12 


11 


42 


12 




18 




397 


284 


197 



32 
THE FOURTH EXPERIMENT. 
In order to determine the interval at which facts once 
well known should be repeated in order that they may not be 
forgotten, it seemed expedient to use the facts that Uad been 
learned in the previous experiments. The facts used in the 
second were at one time known to the children, and the ex- 
perimenter had positive knowledge of the conditions under 
which they were learned. It was therefore arranged to call 
for a repetition of these facts at varying intervals. 

Ihe results of these repetitions follow. They are headed 
respectively : Results with ITgh School, Results with A 
Grammar School, and Results with Seventh Grade, A and B 
Divisions. 

Since the facts of the second experiment were rather 
difficult to learn, and since the conditions under which they 
would be forgotten would probably differ somewhat from the 
manner of forgetting things learned under ordinary school 
conditions, it was decided that in this attempt at determining ' 
the length of the interval, it would be well to use also the facts 
of the third experiment which were regularly learned as school 
lessons as well as the facts used with the fifth grade in the 
first experiment. The fifth grade had, with seeming ease, 
learned the facts presented to them in what seemed to be a 
remarkably short time and there existed an interval of twenty 
months since the last repetition. 

The results of the last mentioned rej^etitions will also be 
found on the following sheets: The sheet containing the re- 
sults obtained with facts of experiment three are so designated, 
and the results obtained with what were fifth grade pupils 
when the facts were given in the first experiment, are headed 
Fifth Grade of 1907, Experiment i ; though it must not be for- 
gotten that these pupils are now seventh grade children, and 
that in the meanwhile they have not studied the Geography of 
South America as a regular school lesson. 

The sheet containing a summarization of the results has 
the summary of the results obtained with each group, sim- 
ilarly designated. 

A glance at the Summary of Results will show the fact 
that the accuracy of the average of errors is dependent upon 
the children who were absent. If the absentees were indi- 
viduals who usually had more than the average number of 
errors, the general average was proportionately lowered, and 
if the absentees were those who usually made less than the 
average number of errors, this general average was increased, 
since their absence would diminish the divisor by one and have 
but little effect upon the dividend. Since, however, in no case 
the absence of any child affected the general average more than 
I, it was considered by the members of the Seminar that this 
cause of variation might be regarded as a negligible factor. 



33 

It will be observed that with the High School, A Grammar 
and Seventh Grades the interval and the average of errors 
is comparatively uniform in the first repetition, and that the 
reduction of the avera^ of errors on the part of the high 
school pupils furnishes an exception in the second. The one 
day interval caused reduction in the average of errors of more 
than ten in each case. A reduction of 1.3 in the average of 
errors is the least reduction that was caused by the thirteen 
day interval ; but that there was a reduction in each case is 
an indication that this interval is too short. 

The twenty-eight day interval caused a reduction with the 
high school and Seventh Grade, B. Division, but a considerable 
increase in A Grammar. The A Grammar furnishes another 
exception in that it indicates a reduction in the average of 
errors w^hen the interval is nearly twice as long. This would 
indicate that the increase of the average in the former repe- 
tition was probably due to some disturbing factor and the 
conclusion could still be drawn that an interval of a month 
is not too long. 

In the Seventh Grade, A Division, the interval was made 
seventy- four days and the average of errors is nearly doubled. 
In the Seventh Grade, B Division, an interval of thirty-nine 
days and of forty days caused a reduction. Thirty day inter- 
val which was fixed between the last repetition caused con- 
siderable reduction in each case except with the Seventh 
Grade, B Division, where it remained the same. 

It will be noticed that the reduction in each case in the 
last repetition is quite considerable except in the case of the 
Seventh Grade. B Division, where there is no change. It will 
also be seen that there is sl reduction in every case where the 
interval was less than fifty days except in tli^ forty-nine day 
interval with the high school. 

Though it by no means follows as an undeniable conclu- 
sion, the inference at least seems justifiable, that with a repe- 
tition interval of about sixty days, the average of error will re- 
main fairly constant. In consideration of the rapid decreases in 
the last repetitions, the experimenter feels free to believe that 
this interval could be increased in arithmetical ratio, in which 
five days would represent the common difference of the vary- 
ing intervals. 

In the opinion of the experimenter, the inference and the 
belief alx)ve stated are confirmed by the results summarized 
under. Fifth Grade of 1907 and Facts of Experiment Three, 
even though the twenty-eight day interval would sewn to be 
an exception. 



34 

Results with Hijrh School 



I 


21 








1 


3 








2 


8 


2 


6 


4 


II 


6 





3 


19 


3 








2 








4 


23 








3 


9 








5 


26 


4 




3 


10 


2 





6 


28 


8 


4 


5 


14 


8 


8 


7 




2 





2 










8 


31 


16 


5 


7 


7 


3 


3 


9 


21 


6 


2 


I 


I 







lO 


32 


7 


6 


3 


3 


2 





ri 


12 














2 





12 


10 



















13 


18 


13 




13 


7 




2 


14 


28 


15 


8 


15 


15 


9 


3 


15 


12 


I 

















16 


29 








I 





I 





17 


12 


I 





4 


2 


2 





18 


22 






2 


2 








19 


16 


5 


3 


5 


2 





4 


20 


25 


2 


I 


I 


I 








21 


4 


4 





I 











22 


39 


9 


4 


7 


8 


7 


3 


23 


21 




5 


7 


8 


7 


I 


24 


30 


5 


I 


2 


I 








25 


22 


4 







5 






26 


17 


2 


2 


4 


5 


3 




27 


23 


5 


3 


3 


4 


I 


4 


28 


14 




















29 


23 
















I 


30 


30 


3 


3 


2 











31 


15 





2 


1 











32 


22 





2 














33 


22 


II 


6 


4 








2 


34 


13 














2 




35 


22 







I 











36 


4 








2 











37 


32 


8 


8 




II 


3 




38 


11 




















39 


9 








I 


I 








40 


13 














3 


I 


41 


9 





T 











I 


42 


31 


10 


5 


5 


13 


5 





43 


4 


6 

















44 


26 


I 


I 






12 


3 


45 


27 


5 




3 




I 





46 


27 


4 











2 





47 


27 


10 


5 






8 





930 172 83 113 145 89 36 



35 

Results with A Grammar 



I 27 


8 


3 


4 


7 


4 


4 


2 34 


18 


10 


10 


4 


8 


4 


3 28 


12 


6 










4 23 


5 


2 




4 


3 


4 


5 23 


10 


10 


II 


II 




8 


6 23 




17 


II 


16 


23 




7 24 


II 


5 


12 


8 


3 


2 


8 28 


17 


11 


7 


II 




3 


9 31 


18 


16 


16 


7 


13 




10 9 


I 






5 


I 





II 31 


9 


6 


4 


7 


4 


3 


12 19 




6 


I 


I 








13 22 






19 


22 


20 


12 


H 2Z 


II 


10 




9 






15 32 


20 


15 


17 


13 


7 


8 


16 22 


4 


2 




3 




5 


17 20 


16 


13 


14 


9 


9 


2 


J8 35 


23 


17 


15 


15 


15 


13 


19 24 


16 


II 


4 


I 




4 


20 25 


17 


15 


16 


16 


15 


6 


21 . . 




21 


18 


15 


10 


9 


22 23 


7 





5 


2 





2 


2^^ 16 


3 


I 


I 


1 








24 20 


6 




4 


I 





2 


25 30 


18 


5 


12 


10 


II 


10 


26 29 


16 


8 


17 


16 


13 


12 


27 16 


II 


4 


9 


7 


4 


3 


28 28 


9 


3 


3 


6 


2 





29 32 


18 


17 


16 


17 




17 


30 29 


19 


12 


12 


II 






31 2^: 


II 


3 


13 


12 


9 


5 


2,2 21 


19 


4 


13 


2 


5 


13 


Zd, 20 


6 


8 


5 


3 


6 





34 22 


8 


8 


5 


6 


7 




35 18 


6 


^ 


2 


I 





2 


36 20 


6 


6 


13 


6 






37 29 


12 


12 


8 


9 


2 


3 



884 391 290 317 294 194 156 



36 
Results with Seventh Grade 
Seventh Grade- B Division Seventh Grade- A Division 



(NJ — ^ 



I 


30 


16 


12 


11 


7 


9 


5 


I 


23 


8 





3 








2 


23 


6 


5 


I 


2 




I 


2 


17 


3 













3 




15 


9 


17 


14 


13 


9 


3 


?>7 


16 


15 


31 


23 


15 


4 


26 


10 


14 


10 


7 


I 


5 


4 


31 


11 


2 




3 


7 


5 


7 





6 


4 


I 


I 





5 


23 


10 





3 




2 


6 


16 


9 


10 


7 


8 


5 


5 


6 


26 


18 


6 


12 


8 


7 


7 


19 


3 


2 





2 


3 





7 


29 


7 


3 




12 


6 


8 


16 


8 


8 


10 


2 


3 


4 


8 


17 


6 


7 


10 




3 


9 


10 


I 


I 








I 





9 


26 


17 


8 


21 


19 


19 


lO 


24 


8 


6 


4 


5 





4 


10 


34 


20 




16 


II 


23 


II 


II 


5 





I 











II 


26 


7 


9 


10 


12 


4 


12 


25 


6 


6 


I 


I 


1 


3 


12 


29 


10 








4 


6 


13 


28 


II 


13 


8 


8 


6 


3 


13 


22 


9 




9 


I 





14 


17 


9 





II 


10 


4 


8 


14 


20 


16 


15 


13 








15 


17 


10 


II 


2 


9 







15 


19 


6 


10 


7 


5 


8 


16 


24 


7 


5 


3 


4 


4 


3 


16 


31 


18 


14 


26 


22 


18 


17 


36 


14 


15 


7 


4 


16 


9 


17 


20 


7 





3 








18 


19 


4 


5 


4 


3 


3 




i-a 


22 


15 


8 


6 


9 


2 


19 


26 


19 




22 


20 


5 


14 


19 


18 


8 


3 


10 


I 





20 


23 


5 


5 


2 


2 





. . 


20 


II 







I 





I 


21 


20 


6 


5 


4 


4 





I 


21 


16 


6 


3 










22 


30 


18 


16 


12 


12 


2 


3 


22 


23 


10 


2 





9 







448 


190 


154 


141 


125 


77 


77 


n 

24 
25 


23 

25 
26 


7 

6 


9 

5 
8 


2 

15 
18 


10 
II 


6 
17 



594 241 127 206 160 144 



37 

c 



=1 

• o. 




tal Numl 
Errors 

erage of 
rors 

ngth of 
:erval 


3 (U 


d 
Z 


c^ > «- <u c 

(- <u -J - 
High School 


I 


46 


930 20.2 224 days 


2 


44 


172 3.9 I day 


3 


41 


83 2.02 13 days 


4 


44 


113 2.5 28 days 


5 


44 


145 3-3 49 days 


6 


43 


89 2.07 30 days 


7 


41 


36 .88 30 days 
A Grammar 


I 


36 


884 24.5 227 days 


2 


33 


391 11.8 I day 


3 


34 


290 8.5 13 days 


4 


32 


317 9.9 28 days 


5 


36 


294 8.16 49 days 


6 


26 


194 7.46 30 days 


7 


30 


156 5.2 29 days 


Seventh Grade- A Division 


I 


25 


594 23.7 237 days 


2 


24 


241 10.04 I day 


3 


23 


127 5-5 13 days 


4 


22 


206 9.36 74 days 


5 


22 


160 7.27 33 days 


6 


23 


144 6.26 30 days 


Seventh Grade- B Division 


I 


21 


448 21.3 237 days 


2 


22 


190 8.6 I day 


3 


21 


154 7-3 13 days 


4 


22 


141 6.4 28 days 


5 


22 


125 5.68 39 days 


6 


20 


-j-j 3.8 40 days 


7 


20 


jy 3.8 29 days 




Fifth Grade of 1907 


Facts 


5 of First Experiment 


1 


35 


416.5 1 1.9 2omos. 


2 


35 


90.83 2.59 2 days 


3 


35 


98 2.8 28 days 


4 


34 


63.3 1.8 30 days 




Results with Facts of 




Bxperinient Three 


I 


41 


397 9-7 9-5 mos. 


2 


40 


284 6.5 64 days 


3 


38 


197 5.2 53 days 



LIBRARY OF CONGRESS 




